Consider the curve r(t) = (sin(2t - 2), In(t+1)), t> -1. (a) Find the tangent vector for r(t). (b) In what direction is a particle on the curve moving at t = 1? (c) Is a particle on the curve moving faster at t= 1 or t=2? Justify your answer. Consider the surface f(x, y) = 2+1 (a) Compute fy (b) Suppose you are standing on this surface at the point (1,2, f(1, 2)) and take an infinitesimally small step in the positive y direction. Would you have moved uphill, downhill, or would your elevation have stayed the same? Justify your answer.